1,721,154 research outputs found
Orbital Stability of ground state solutions of coupled nonlinear Schr"odinger equations
No full textOrbital stability property for weakly coupled nonlinear
Schrodinger equations is investigated. Different families of orbitally stable standing waves solutions will be found, generated by different classes of solutions of the associated elliptic problem. In particular, orbitally stable standing waves can be generated by least action solutions, but also by solutions with one trivial component whether or not they are ground states. Moreover, standing waves with components propagating with the same frequencies are orbitally stable if generated by vector solutions of a suitable Schro ̈dinger weakly coupled system, even if they are not ground states
Weakly coupled nonlinear Schrodinger systems: the saturation effect
No full textWe study the existence of solutions for a class of saturable weakly coupled Schrödinger systems. In most of the cases we show that least energy solutions have neces- sarily one trivial component. In addition sufficient conditions for the existence of a solution with both positive components are found
Positive solutions for a weakly coupled nonlinear Schrodinger system
No full textExistence of a nontrivial solution is established, via variational methods, for a system of weakly coupled nonlinear Schrodinger equations. The main goal is to obtain a positive solution, of minimal action if possible,
with all vector components not identically zero. Generalizations for nonautonomous systems are considered
Energy convexity estimates for non degenerate ground states of nonlinear 1D Schrodinger systems
No full textWe investigate the modulational stability for a class of 1D semilinear Schrodinger system
Orbital Stability of ground state solutions of coupled nonlinear Schr"odinger equations
No full textOrbital stability property for weakly coupled nonlinear
Schrodinger equations is investigated. Different families of orbitally stable standing waves solutions will be found, generated by different classes of solutions of the associated elliptic problem. In particular, orbitally stable standing waves can be generated by least action solutions, but also by solutions with one trivial component whether or not they are ground states. Moreover, standing waves with components propagating with the same frequencies are orbitally stable if generated by vector solutions of a suitable Schro ̈dinger weakly coupled system, even if they are not ground states
Weakly coupled nonlinear Schrodinger systems: the saturation effect
No full textWe study the existence of solutions for a class of saturable weakly coupled Schrödinger systems. In most of the cases we show that least energy solutions have neces- sarily one trivial component. In addition sufficient conditions for the existence of a solution with both positive components are found
Semilinear Hamiltonian Schrödinger Systems
No full textIn this paper we investigate on local and global existence for
some semilinear Schrödinger systems having conservation of the energy and
masses. Moreover we presents some blowing up examples for 2 × 2 systems
Blow up analysis, existence and qualitative properties of solutions for the two dimensional Emden-Fowler equation with singular potential
No full textMotivated by the study of a two-dimensional point vortex model, we analyze the following Emden-Fowler type problem with singular potential
\bgin{equation}\graf{
-\lapl u=\lm \dfrac{\e{u}}{\ino\e{u} \dx} & \mbox{in}\hspace{.2cm} \om,
\nonumber\\\\
\hspace{.55cm}u=0 & \hspace{-.05cm} \mbox{on}\hspace{.2cm} \om,
}\end{equation}
where \displaystyle V(x)=\frac{ K(x)}{|x|^{2\al}} with , 0< a\leq K(x)\leq b<+\infty, \fal{x}{\om} and \|\nabla K\|_\i\leq C.
We first extend various results, already known in case , to cover the case . In particular, we study the concentration-compactness problem and the mass quantization properties, obtaining some existence results.
Then, by a special choice of , we include the effect of the angular momentum in the system and obtain the existence of axially symmetric one peak non radial blow up solutions
On the shape of blowup solutions to a mean field equation
No full textWe analyze the structure of non radial -point blow up solutions sequences for the Liouville type equation on the two dimensional unit disk,
-\lapl u(x)=\la \dfrac{\e{u(x)}}{\inb\e{u(x)} \dx}\;\;\mbox{in}\;\; D,
\;\;u(x)=0\;\;\mbox{on}\;\; D.
In case , we provide necessary and sufficient conditions for the existence of blow up solutions and, in the same spirit of \cite{cl1}, prove their axial symmetry with respect to the diameter joining the maximum points.
Finally, we prove that a non radial one point blow up solution exists only if \la-8\pi>0
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